Is csc(x)+cot(x)=(sin(x))/(1-cos(x)) ?

The answer to whether csc(x)+cot(x)=(sin(x))/(1-cos(x)) is True

Popular >

prove csc(x)+cot(x)=(sin(x))/(1-cos(x))

prove

csc (x) + cot (x) = \frac{sin ( x )}{1 - cos ( x )}

True

Solution steps

csc (x) + cot (x) = \frac{sin ( x )}{1 - cos ( x )}

Manipulating left side

csc (x) + cot (x)

Express with sin, cos

= \frac{1 + cos ( x )}{sin ( x )}

Manipulating right side

\frac{sin ( x )}{1 - cos ( x )}

Rewrite using trig identities

= \frac{1 + cos ( x )}{sin ( x )}

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (x) = \frac{1}{2} (1 + cos (2 x))

sin (2 x) = sin (x + x)

8 cos^{4} (x) - 8 cos^{2} (x) + 1 = cos (4 x)

\frac{cos ( 2 x ) - cos ( 4 x )}{sin ( 2 x ) sin ( 4 x )} = tan (x)

\frac{tan ( x ) + cot ( x )}{csc ( x )} = sec (x)

Is csc(x)+cot(x)=(sin(x))/(1-cos(x)) ?
The answer to whether csc(x)+cot(x)=(sin(x))/(1-cos(x)) is True